The title is that of a course with the same name, designed for teachers of mathematics. The rational for a course specifically on geometry was that "many of those currently teaching mathematics in school had little geometrical education". Teachers on the course experience geometry through problem solving, and learning to pose geometrical problems.…

In "MT218" the author looked at the possibility of basing a classroom activity on a simple, though not totally transparent, number-theoretic result. In this article he considers another relatively straightforward idea from number theory that could be used either as a lesson starter or as the basis of a more substantial task, requiring students to…

In this article, the author explores what Assessing Pupils' Progress (APP) is about. He contends that the predilection for testing is a catastrophe as far as the teaching and learning of mathematics is concerned; it is an outcome of the drive for collecting so-called "data" on pupils. What those people, who should know better, either choose to…

This article is the third in a series which draws on findings from Nunes, Watson and Bryant (2009): "Key understandings in school mathematics: a report to the Nuffield Foundation". In this article the author focuses on what learners have to understand and learn in order to do secondary mathematics well in general terms. She is assuming a…

The field of mathematics is complex, areas such as arithmetic, and geometry each consist of several sub-domains and encompass many cognitive processes. Achievement tests for elementary pupils assess a wide range of arithmetic skills such as number sense, procedural knowledge, and using problem solving strategies. Although mathematical tests often…

"The power of two" is a Royal Institution (Ri) mathematics "master-class". It is a two-and-a half-hour interactive learning session, which, with varying degree of coverage and depth, has been run with students from Year 5 to Year 11, and for teachers. The master class focuses on an historical episode--the Josephus…

Over the past three years this author has spent a good deal of time in primary classrooms, working with teachers on problem solving approaches to the teaching and learning of mathematics. He has also worked part-time on an initial teacher training course and an NCETM/Yorkshire Forward funded project entitled "Inspiring Mathematics Champions". Thus…

Stresses the need for theories of teaching and learning mathematics. Argues that a study of how students react to new problem solving situations is a step in the right direction. (RS)

Two problem-solving strategies involved in finding the area of a particular square formed on a geoboard are described in detail. (MP)

Decision exercises using a finite state machine and replacement systems are described in this second of two articles. For the first article, see MT No. 62, March, 1973, pp. 50-55. (DT)

The problem of inscribing a square in a semicircle and related problems are discussed. Solutions to the problems are provided. (FL)

A discussion of what constitutes proof is given. Methods of teaching proof in a more intuitive and informal way than is usually done are suggested. (MK)